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A137214 a(n) is the number of distinct decimal digits in 2^n.

%I A137214 #19 Jul 24 2021 03:12:53
%S A137214 1,1,1,1,2,2,2,3,3,3,4,4,4,4,5,5,3,5,4,4,7,6,5,4,4,4,6,6,6,9,7,7,5,6,
%T A137214 6,7,7,8,7,7,7,6,8,7,9,8,7,8,9,7,8,9,8,7,7,8,8,7,9,8,9,9,9,9,9,9,8,9,
%U A137214 10,9,10,7,9,8,9,9,9,8,9,10,9,9,10,9,10,9,9,10,10,10,9,8,9,9,10,10,10,10,10
%N A137214 a(n) is the number of distinct decimal digits in 2^n.
%C A137214 Appears to be all 10's starting at a(169). - _T. D. Noe_, Apr 01 2014
%H A137214 T. D. Noe, <a href="/A137214/b137214.txt">Table of n, a(n) for n = 0..1000</a>
%F A137214 a(n) = A043537(2^n). - _R. J. Mathar_, Mar 16 2008
%e A137214 a(16) = 3 because 2^16 = 65536, which contains 3 distinct decimal digits [3,5,6].
%p A137214 A043537 := proc(n) nops(convert(convert(n,base,10),set)) ; end: A137214 := proc(n) A043537(2^n) ; end: seq(A137214(n),n=0..120) ; # _R. J. Mathar_, Mar 16 2008
%p A137214 a:=proc(n) options operator, arrow: nops(convert(convert(2^n,base,10),set)) end proc: seq(a(n),n=0..80); # _Emeric Deutsch_, Apr 02 2008
%t A137214 Table[Length[Union[IntegerDigits[2^n]]], {n, 0, 100}] (* _T. D. Noe_, Apr 01 2014 *)
%o A137214 (Python)
%o A137214 def a(n): return len(set(str(2**n)))
%o A137214 print([a(n) for n in range(99)]) # _Michael S. Branicky_, Jul 23 2021
%Y A137214 Cf. A043562, A043536.
%K A137214 easy,nonn,base
%O A137214 0,5
%A A137214 _Ctibor O. Zizka_, Mar 06 2008
%E A137214 More terms from _R. J. Mathar_ and _Emeric Deutsch_, Mar 16 2008